Join-Principal Element Lattices
E. W. Johnson · Proceedings of the American Mathematical Society · 1976
Let $(\mathfrak {L},M)$ be a local Noether lattice. If the maximal element $M$ is meet principal, it is well known and easily seen that every element of $\mathfrak {L}$ is meet principal. In this note, we obtain the corresponding result for $M$ join-principal. We also consider join-principal elements generally under the assumption of the weak union condition and show, for example, that the square of a join-principal element is principal.